Solve the following equation for x. Express your answer in the simplest form.
3(-7x-6)=-2(x-6)
Expanding both sides of the equation, we have:
-21x - 18 = -2x + 12
Adding 2x to both sides, we get:
-19x - 18 = 12
Adding 18 to both sides, we get:
-19x = 30
Dividing both sides by -19, we find:
x = -30/19
what would x equal if there was only one solution?
If there is only one solution, it means that the equation has only one possible value for x. To find this value, we can continue solving the equation:
-21x - 18 = -2x + 12
Adding 2x to both sides:
-19x - 18 = 12
Adding 18 to both sides:
-19x = 30
Dividing both sides by -19:
x = -30/19
Therefore, the value of x when there is only one solution is x = -30/19.
Solve the following equation for x. Express your answer in the simplest form.
3(x-2)=3x-7
Let's begin solving the equation step-by-step:
3(x-2) = 3x-7
First, distribute the 3 to both terms inside the parentheses:
3x - 6 = 3x - 7
Next, subtract 3x from both sides to move the variable terms to one side:
-6 = -7
Since the equation -6 = -7 is not true, this implies that there is no value of x that satisfies the equation. Therefore, there is no solution for this equation.
Autumn has a points card for a movie theater.
She receives 40 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 225 points for a free movie ticket.
Write and solve an inequality which can be used to determine vv, the number of visits Autumn can make to earn her first free movie ticket.
Let's denote vv as the number of visits Autumn can make to earn her first free movie ticket. To determine the inequality, we can use the information given in the problem.
Autumn receives 40 rewards points just for signing up and earns 12.5 points for each visit. Therefore, the total number of points Autumn will have after vv visits can be calculated as:
Total Points = 40 + 12.5*vv
Since Autumn needs at least 225 points for a free movie ticket, we can set up the following inequality:
40 + 12.5*vv ≥ 225
To solve for vv, we need to isolate the variable by subtracting 40 from both sides:
12.5*vv ≥ 225 - 40
12.5*vv ≥ 185
Finally, divide both sides by 12.5 to solve for vv:
vv ≥ 185 / 12.5
vv ≥ 14.8
Since vv represents the number of visits, and we cannot have a fraction of a visit, Autumn would need to make at least 15 visits to earn her first free movie ticket.